Anagrams were very popular during the 17th century, and particularly in France. King Louis XIII used anagrams as a recreational form of intellectual stimulation and source of entertainment for himself and members of his court. He formed some on his own and hired a Royal Anagrammatist whose sole task was to devise anagrams. A lot of these anagrams were based on the names of people, and particularly, on the name of the king with the theme being how great he was.
The book "Of Anagrams" by Henry Benjamin Wheatley (downloadable for free from its Google Books entry) says that "Anagrams were used by fine gentlemen to add pungency to their conversation". It cites Henry Peacham's "Compleat Gentleman" (written in 1634) which basically says that among the conversational skills of a gentleman ("merry tales, wittie questions and answers", "ingenious epigrams") should be the spontaneous spouting of anagrams. He gives the example of someone who was going to say "I must goe buy a dagger" but decided to switch around the letters and say "I must goe dye a beggar". [It's not strictly an anagram though; it's actually a rearrangement of sounds. A more precise description might be "anaphone".]
In the 19th century, it was popular to anagram the names of famous people (celebrities, I suppose). Lewis Carroll produced many such anagrams, including Florence Nightingale ("Flit on, cheering angel."), Disraeli ("I lead, sir."), and a politician of the time named William Ewart Gladstone ("Wild agitator means well!"). The popularity of anagramming at the time led to the Victorian game of Anagrams (previously described here and which now is sold under the name "Snatch") which was played by Alfred Butts as a child. His first attempts at inventing a game drew inspiration from the idea of anagramming as the basis of a game, to which he added a letter distribution like that of the English language. After a few more iterations, he converged on the game of Scrabble, which led to Speed Scrabble, which led to Bananagrams.